- Email: [email protected]
Hadronic B Decays from Belle
Nuclear Physics B (Proc. Suppl.) 164 (2007) 181–184 www.elsevierphysics.com
Hadronic B Decays from Belle Mikihiko Nakaoa∗ a
KEK, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki, 305-0801 Japan The latest results on hadronic B meson decays from the Belle experiment are discussed and summarized. The selected topics are charmless B meson decays into two-, three- and four-body final states of kaons and pions, and baryonic B meson decays.
1. Introduction The Belle experiment at the KEKB e+ e− asymmetric energy B factory has collected more than 400 fb−1 of data of which 357 fb−1 has been analyzed (referred to as the full dataset). This dataset contains 386 million BB (B 0 B 0 and B + B − ) events.2 Decays of the B meson provide a rich playground for low energy QCD effects. For example, higher order QCD corrections are already essential ingredients to study the semileptonic (b → (c, u)ν), radiative (b → (s, d)γ) and electroweak (b → s+ − ) processes. The goal is to precisely confirm the Standard Model predictions, and to search for new physics effects as deviations from the Standard Model. These modes are considered to be theoretically clean, thanks to the existence of leptons or a photon, but the number of channels and observables are limited. There are numerous hadronic B decay channels for which the branching fractions have been precisely measured. In principle one can extract fundamental physics quantities out of the observables of hadronic B decays according to the factorization hypothesis. It is however difficult to reliably predict a branching fraction for a hadronic mode even for a simple one such as B 0 → K + π − due to various QCD effects. There are several theoretical frameworks to include perturbative and non-perturbative QCD corrections to the factorization, such as the QCD factorization, the p∗ on
behalf of the Belle Collaboration. of the results discussed in this report are based on a smaller dataset. 2 Some
0920-5632/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2006.11.090
QCD approach and the soft collinear effective theory, but none of them so far successfully describe the entire structure of the available data [1]. The quantities like ratios of branching fractions, CP asymmetry and polarization are easier to predict due to the cancelation of various non-perturbative uncertainties. In addition to the many branching fraction results that have been provided by the Bfactory experiments, measurements of the other quantities are recently getting available. 2. Two-body Charmless B Decays The set of two-body charmless B decays into pions and kaons (B → Kπ, B → ππ and B → KK) provides an ideal sample to understand the short distance tree, penguin and other smaller amplitudes. Major contributions are the b → s penguin to the B → Kπ modes, b → u tree to the B → ππ and B → K + π modes, b → d penguin to the B → ππ and B → K 0 K modes, while only the highly suppressed exchange diagram contributes to the B 0 → K + K − mode. For the modes with two or more amplitudes, both the strong and weak phase can be different for every amplitude, and the interference of amplitudes can cause direct CP violation. One such example is B 0 → K + π − , which has tree and penguin amplitudes whose weak phases differ by the unitarity angle φ3 . Measurement of direct CP asymmetry in B 0 → + − K π is updated with the full dataset. As shown in Fig. 1, we clearly observe the difference in the size of the signal. The new result [2] is ACP (B 0 → K + π − ) = −0.113 ± 0.022 ± 0.005
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M. Nakao / Nuclear Physics B (Proc. Suppl.) 164 (2007) 181–184
branching fraction is expected to be very small, a very strict upper limit of 3.7 × 10−7 (90% C.L.) is set.
700 600
Entries/20MeV
Entries/20MeV
with about 5σ statistical significance (the first and second errors are statistical and systematic throughout the report). The result is consistent with the previously available results last year, and is the most significant direct CP asymmetry in B decays.
K−π+
500 400 300
700 600
400 300 200
100
100 0
0.5
K+π−
500
200
0
3. Three-body Charmless B Decays
0
0
ΔE (GeV)
0.5
ΔE (GeV)
Figure 1. ΔE distribution of the B 0 → K − π + and B 0 → K + π − events. Dashed line shows the signal component.
The same short distance amplitudes are expected to contribute to a similar decay mode, B + → K + π 0 . The new result [2], ACP (B + → K + π 0 ) = +0.04 ± 0.04 ± 0.02, is however deviated from B 0 → K + π − by 3.1σ. Most of the predictions give similar values and the same sign of asymmetry for these two modes in contrast with the measured values. The deviation could be a clue to deepen our understanding of the QCD based predictions or a hint for a new physics effect. For example, an electroweak penguin type contribution from new physics can generate such a difference. In addition to the already measured four B → Kπ and three B → ππ modes, we found evidence for B + → K + K 0 and B 0 → K 0 K 0 modes that proceed via the b → d transition and thus suppressed with respect to the other two-body decay modes. The measured branching fractions are B(B + → K + K 0 ) = (1.0 ± 0.4 ± 0.1) × 10−6 and B(B 0 → K 0 K 0 ) = (0.8 ± 0.3 ± 0.1) × 10−6 with 3.0σ and 3.5σ significances, respectively [3]. For the remaining B 0 → K + K − mode, whose
A Dalitz analysis of the three-body charmless B decay mode is the essential method to decompose the contributions of various interfering amplitudes of quasi-two-body decays such as B → ρK, B → K ∗ π, B → f0 K, and so on. We have extended the Dalitz analysis to search for CP violating amplitudes in B ± → K ± π ± π ∓ with the full dataset, by dividing the sample into B + and B − and assuming that the phase and amplitude for every quasi-two-body channel can be different between B + and B − [4]. Direct CP violation can occur both in the size and phase of the quasi-two-body amplitudes. In the former case, direct CP violation occur in a quasi-two-body decay mode which provide information to understand the short distance amplitudes. In the latter case, direct CP violation in the Dalitz plane can occur even when the direct CP violation is missing in any of the quasi-twobody decay modes. The Dalitz distribution is well described by a mixture of K ∗0 π + , K0∗ (1430)π + , ρ0 K + , ωK + , f0 K + , f2 (1270)K + , χc0 K + and fX (1300)K + final states and a non-resonant component as shown in Fig. 2. Here, fX (1300) is an unknown state with a mass around 1.45 GeV and a width of 126 MeV from the fit. Among these modes, we find evidence for large direct CP violation in the B + → ρ0 K + mode, +0.11 ACP (B + → ρ0 K + ) = 0.30 ± 0.11 ± 0.03 −0.04 ,
with a 3.9σ significance. Here, the third error is a model error due to the choice on the contributing amplitudes, which is small enough to validate the assumed model. This is the first time to report large CP violation in charged B decays. 4. Four-body Charmless B Decays The four-body charmless B decay modes are similarly composed of quasi-two- and three-body decays. The most interesting modes are quasitwo-body decays into vector-vector (VV) final
M. Nakao / Nuclear Physics B (Proc. Suppl.) 164 (2007) 181–184
still confirm that the fL for B → φK ∗ modes are significantly smaller than unity. The situation is different for B → ρρ decays that give fL ∼ 1 [6]:
300 160 140
2
Events/(0.05 GeV/c )
180
(a)
250
120 100
200
80
fL (B + → ρ+ ρ0 ) = 0.95 ± 0.11 ± 0.02, +0.03 ± 0.03. fL (B 0 → ρ+ ρ− ) = 0.95 −0.04
60 40
150
20 0 0.6
0.8
1
1.2
1.4
1.6
1.8
100
The main difference is that the former proceed through the b → s penguin transition while the latter through the b → u tree. One attractive explanation for this “VV polarization puzzle” is a new physics effect in the penguin diagram that may have a different amplitude structure. It was suggested to measure all the other observables in terms of triple products; no inconsistency has been found to suggest such an effect. We have also measured fL for another b → s mode [7],
50 0
1
2
3 4 M(K+π-) (GeV/c2)
5
350 25
(b)
Events/(0.05 GeV/c2)
300
20
250
15 10
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0
100
+0.05 fL (B + → K ∗0 ρ+ ) = 0.43 ± 0.11 −0.02 ,
50
which is also much smaller than unity.
3.2
0
0
1
183
3.3
3.4
2 3 M(π+π-) (GeV/c2)
3.5
3.6
4
5
Figure 2. K ± π ∓ and π ± π ∓ projections of the B ± → K ± π ± π ∓ Dalitz plane for the data points and fit results (histogram).
states since due to the freedom of the polarization there are three helicity (or transversity) amplitudes from which one can construct 11 independent observables if CP violation is allowed. The vector states we consider are ρ, K ∗ and φ. The first measured observable was the fraction of the longitudinal polarization fL . It has been naively predicted that the longitudinal amplitude dominates, since it does not involve a spin-flip of quarks while two other transverse amplitudes require to flip the spin of one or two quarks. The situation is the same for the most of the QCDcorrected factorization predictions. Therefore it drew a lot of attention when fL was found to be about 0.5 in B → φK ∗ decays. The latest Belle results [5], fL (B 0 → φK ∗0 ) = 0.45 ± 0.05 ± 0.02, fL (B + → φK ∗+ ) = 0.52 ± 0.08 ± 0.03,
5. Baryonic B Decays We have extensively measured B decay modes of various types that involve a baryon-pair in the final state. Modes with the b → c, b → s and b → u transitions are observed in two- (only for b → c), three- and four-body decays. This is a crucial set of samples to understand the mechanism of B decays, as well as for baryon spectroscopy and new particle hunting. For charmed baryonic decays, there is a clear hierarchy in the branching fractions [8], +5.6 −6 B(B 0 → Λ− , c p) = (21.9 −4.9 ± 6.5) × 10 + − + B(B → Λc pπ ) = (201 ± 105 ± 56) × 10−6 , + − −6 . B(B 0 → Λ− c pπ π ) = (1030 ± 90 ± 295) × 10
A similar hierarchy is observed in charmless baryonic decays. Two-body final states have not been observed yet with upper limits around 5 × 10−7 [9], while the branching fractions with threebody final states are around 1–5×10−6, and the branching fraction for the first four-body final state, ppK ∗+ , is about 10 × 10−6 [10]. Another interesting feature that is commonly observed in all baryonic three-body decay modes is the threshold enhancement just above the baryon-pair mass. In order to understand the
184
M. Nakao / Nuclear Physics B (Proc. Suppl.) 164 (2007) 181–184
effect, we have measured the decay angle distribution. In the case of B + → ppK + , the distribution of the cosine of the p decay angle with respect to K + shows a strong peak towards 1, and therefore the enhancement is likely to be due to a fragmentation effect. On the other + hand, in the case of B + → Λ− c pπ , the enhancement could be a new narrow bound state, since no obvious angular structure was found, with a +0.01 ± 0.02 GeV and a width of mass of 3.35 −0.02 +0.04 0.07 −0.03 ± 0.04 GeV as shown in Fig. 3.
6. Summary As discussed, Belle has reported large number of results in charmless two-body, three-body and four-body decays and various baryonic decays, among other hadronic decay modes. With the latest dataset, we have established direct CP violation in two- and three-body B decays, while the VV polarization puzzle stays with new results. Exploration of baryonic B decays continues, revealing the structure which seems to be quite different from mesonic decays.
2
Events/(0.05 GeV/c )
REFERENCES 25 20 15 10 5 0 3.2
3.4
3.6
3.8
4
4.2
4.4
4.6 –
4.8
5 2
M(Λ+cp) (GeV/c )
Figure 3. + Λ− c pπ .
+ Λ+ → c p mass distribution in B
We have also reported the observations of doubly charmed baryonic decay modes, B + → − + 0 + − 0 + Λ+ → Ξ0c Λ+ c Λc K , B → Λc Λc K [11], B c 0 − + and evidence for B → Ξc Λc [12]. The branching fractions for the first two are B(B + → +1.0 − + −4 Λ+ and c Λc K ) = (6.5 −0.9 ± 0.8 ± 3.4) × 10 +2.9 0 + − 0 B(B → Λc Λc K ) = (7.9 −2.3 ±1.2±4.2)×10−4, and the product branching fractions for the lat0 + − ter two are B(B + → Ξ0c Λ+ c ) × B(Ξc → Ξ π ) = +1.0 −5 0 + (4.8 −0.9 ±1.1±1.2)×10 and B(B → Ξ− c Λc )× +3.7 − + − − B(Ξc → Ξ π π ) = (9.3 −2.8 ± 1.9 ± 2.4)× 10−5, where the third error is due to the uncertainty − + of B(Λ+ c → pK π ). Assuming the theoretical prediction for B(Ξ0c → Ξ+ π − ), we find the −3 B(B + → Ξ0c Λ+ , which is c ) may be a few 10 a significant contribution to the total B decay width, and is much larger than the expectation for a two-body baryonic decay mode.
1. Theoretical works are not cited due to the limited space. Please refer the references in [2]–[12]. 2. Belle Collaboration, K. Abe et al., hep-ex/ 0507045. 3. Belle Collaboration, K. Abe et al., hep-ex/ 0506080, to appear in Phys. Rev. Lett. 4. Belle Collaboration, K. Abe et al., hep-ex/ 0509001. 5. Belle Collaboration, K.-F. Chen et al., hepex/0503013, to appear in Phys. Rev. Lett. 6. Belle Collaboration, J. Zhang et al., Phys. Rev. Lett. 91, 221801 (2003); Belle Collaboration, K. Abe et al., hep-ex/0507039. 7. Belle Collaboration, J. Zhang et al., Phys. Rev. Lett. 95, 141801 (2005). 8. Belle Collaboration, N. Gabyshev et al., Phys. Rev. Lett. 90, 141802 (2003); Belle Collaboration, K. Abe et al., BELLE-CONF-0468. 9. Belle Collaboration, M.-C. Chang et al., Phys. Rev. D 71, 072007 (2005). 10. Belle Collaboration, M.-Z. Wang et al., Phys. Rev. Lett. 92, 171802 (2004); Belle Collaboration, Y.-J. Lee et al., Phys. Rev. Lett. 93, 211801 (2004). 11. Belle Collaboration, K. Abe et al., hep-ex/ 0508015. 12. Belle Collaboration, R. Chistov et al., hepex/0510074.
Hadronic B Decays from Belle Mikihiko Nakaoa∗ a
KEK, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki, 305-0801 Japan The latest results on hadronic B meson decays from the Belle experiment are discussed and summarized. The selected topics are charmless B meson decays into two-, three- and four-body final states of kaons and pions, and baryonic B meson decays.
1. Introduction The Belle experiment at the KEKB e+ e− asymmetric energy B factory has collected more than 400 fb−1 of data of which 357 fb−1 has been analyzed (referred to as the full dataset). This dataset contains 386 million BB (B 0 B 0 and B + B − ) events.2 Decays of the B meson provide a rich playground for low energy QCD effects. For example, higher order QCD corrections are already essential ingredients to study the semileptonic (b → (c, u)ν), radiative (b → (s, d)γ) and electroweak (b → s+ − ) processes. The goal is to precisely confirm the Standard Model predictions, and to search for new physics effects as deviations from the Standard Model. These modes are considered to be theoretically clean, thanks to the existence of leptons or a photon, but the number of channels and observables are limited. There are numerous hadronic B decay channels for which the branching fractions have been precisely measured. In principle one can extract fundamental physics quantities out of the observables of hadronic B decays according to the factorization hypothesis. It is however difficult to reliably predict a branching fraction for a hadronic mode even for a simple one such as B 0 → K + π − due to various QCD effects. There are several theoretical frameworks to include perturbative and non-perturbative QCD corrections to the factorization, such as the QCD factorization, the p∗ on
behalf of the Belle Collaboration. of the results discussed in this report are based on a smaller dataset. 2 Some
0920-5632/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2006.11.090
QCD approach and the soft collinear effective theory, but none of them so far successfully describe the entire structure of the available data [1]. The quantities like ratios of branching fractions, CP asymmetry and polarization are easier to predict due to the cancelation of various non-perturbative uncertainties. In addition to the many branching fraction results that have been provided by the Bfactory experiments, measurements of the other quantities are recently getting available. 2. Two-body Charmless B Decays The set of two-body charmless B decays into pions and kaons (B → Kπ, B → ππ and B → KK) provides an ideal sample to understand the short distance tree, penguin and other smaller amplitudes. Major contributions are the b → s penguin to the B → Kπ modes, b → u tree to the B → ππ and B → K + π modes, b → d penguin to the B → ππ and B → K 0 K modes, while only the highly suppressed exchange diagram contributes to the B 0 → K + K − mode. For the modes with two or more amplitudes, both the strong and weak phase can be different for every amplitude, and the interference of amplitudes can cause direct CP violation. One such example is B 0 → K + π − , which has tree and penguin amplitudes whose weak phases differ by the unitarity angle φ3 . Measurement of direct CP asymmetry in B 0 → + − K π is updated with the full dataset. As shown in Fig. 1, we clearly observe the difference in the size of the signal. The new result [2] is ACP (B 0 → K + π − ) = −0.113 ± 0.022 ± 0.005
182
M. Nakao / Nuclear Physics B (Proc. Suppl.) 164 (2007) 181–184
branching fraction is expected to be very small, a very strict upper limit of 3.7 × 10−7 (90% C.L.) is set.
700 600
Entries/20MeV
Entries/20MeV
with about 5σ statistical significance (the first and second errors are statistical and systematic throughout the report). The result is consistent with the previously available results last year, and is the most significant direct CP asymmetry in B decays.
K−π+
500 400 300
700 600
400 300 200
100
100 0
0.5
K+π−
500
200
0
3. Three-body Charmless B Decays
0
0
ΔE (GeV)
0.5
ΔE (GeV)
Figure 1. ΔE distribution of the B 0 → K − π + and B 0 → K + π − events. Dashed line shows the signal component.
The same short distance amplitudes are expected to contribute to a similar decay mode, B + → K + π 0 . The new result [2], ACP (B + → K + π 0 ) = +0.04 ± 0.04 ± 0.02, is however deviated from B 0 → K + π − by 3.1σ. Most of the predictions give similar values and the same sign of asymmetry for these two modes in contrast with the measured values. The deviation could be a clue to deepen our understanding of the QCD based predictions or a hint for a new physics effect. For example, an electroweak penguin type contribution from new physics can generate such a difference. In addition to the already measured four B → Kπ and three B → ππ modes, we found evidence for B + → K + K 0 and B 0 → K 0 K 0 modes that proceed via the b → d transition and thus suppressed with respect to the other two-body decay modes. The measured branching fractions are B(B + → K + K 0 ) = (1.0 ± 0.4 ± 0.1) × 10−6 and B(B 0 → K 0 K 0 ) = (0.8 ± 0.3 ± 0.1) × 10−6 with 3.0σ and 3.5σ significances, respectively [3]. For the remaining B 0 → K + K − mode, whose
A Dalitz analysis of the three-body charmless B decay mode is the essential method to decompose the contributions of various interfering amplitudes of quasi-two-body decays such as B → ρK, B → K ∗ π, B → f0 K, and so on. We have extended the Dalitz analysis to search for CP violating amplitudes in B ± → K ± π ± π ∓ with the full dataset, by dividing the sample into B + and B − and assuming that the phase and amplitude for every quasi-two-body channel can be different between B + and B − [4]. Direct CP violation can occur both in the size and phase of the quasi-two-body amplitudes. In the former case, direct CP violation occur in a quasi-two-body decay mode which provide information to understand the short distance amplitudes. In the latter case, direct CP violation in the Dalitz plane can occur even when the direct CP violation is missing in any of the quasi-twobody decay modes. The Dalitz distribution is well described by a mixture of K ∗0 π + , K0∗ (1430)π + , ρ0 K + , ωK + , f0 K + , f2 (1270)K + , χc0 K + and fX (1300)K + final states and a non-resonant component as shown in Fig. 2. Here, fX (1300) is an unknown state with a mass around 1.45 GeV and a width of 126 MeV from the fit. Among these modes, we find evidence for large direct CP violation in the B + → ρ0 K + mode, +0.11 ACP (B + → ρ0 K + ) = 0.30 ± 0.11 ± 0.03 −0.04 ,
with a 3.9σ significance. Here, the third error is a model error due to the choice on the contributing amplitudes, which is small enough to validate the assumed model. This is the first time to report large CP violation in charged B decays. 4. Four-body Charmless B Decays The four-body charmless B decay modes are similarly composed of quasi-two- and three-body decays. The most interesting modes are quasitwo-body decays into vector-vector (VV) final
M. Nakao / Nuclear Physics B (Proc. Suppl.) 164 (2007) 181–184
still confirm that the fL for B → φK ∗ modes are significantly smaller than unity. The situation is different for B → ρρ decays that give fL ∼ 1 [6]:
300 160 140
2
Events/(0.05 GeV/c )
180
(a)
250
120 100
200
80
fL (B + → ρ+ ρ0 ) = 0.95 ± 0.11 ± 0.02, +0.03 ± 0.03. fL (B 0 → ρ+ ρ− ) = 0.95 −0.04
60 40
150
20 0 0.6
0.8
1
1.2
1.4
1.6
1.8
100
The main difference is that the former proceed through the b → s penguin transition while the latter through the b → u tree. One attractive explanation for this “VV polarization puzzle” is a new physics effect in the penguin diagram that may have a different amplitude structure. It was suggested to measure all the other observables in terms of triple products; no inconsistency has been found to suggest such an effect. We have also measured fL for another b → s mode [7],
50 0
1
2
3 4 M(K+π-) (GeV/c2)
5
350 25
(b)
Events/(0.05 GeV/c2)
300
20
250
15 10
200 5
150
0
100
+0.05 fL (B + → K ∗0 ρ+ ) = 0.43 ± 0.11 −0.02 ,
50
which is also much smaller than unity.
3.2
0
0
1
183
3.3
3.4
2 3 M(π+π-) (GeV/c2)
3.5
3.6
4
5
Figure 2. K ± π ∓ and π ± π ∓ projections of the B ± → K ± π ± π ∓ Dalitz plane for the data points and fit results (histogram).
states since due to the freedom of the polarization there are three helicity (or transversity) amplitudes from which one can construct 11 independent observables if CP violation is allowed. The vector states we consider are ρ, K ∗ and φ. The first measured observable was the fraction of the longitudinal polarization fL . It has been naively predicted that the longitudinal amplitude dominates, since it does not involve a spin-flip of quarks while two other transverse amplitudes require to flip the spin of one or two quarks. The situation is the same for the most of the QCDcorrected factorization predictions. Therefore it drew a lot of attention when fL was found to be about 0.5 in B → φK ∗ decays. The latest Belle results [5], fL (B 0 → φK ∗0 ) = 0.45 ± 0.05 ± 0.02, fL (B + → φK ∗+ ) = 0.52 ± 0.08 ± 0.03,
5. Baryonic B Decays We have extensively measured B decay modes of various types that involve a baryon-pair in the final state. Modes with the b → c, b → s and b → u transitions are observed in two- (only for b → c), three- and four-body decays. This is a crucial set of samples to understand the mechanism of B decays, as well as for baryon spectroscopy and new particle hunting. For charmed baryonic decays, there is a clear hierarchy in the branching fractions [8], +5.6 −6 B(B 0 → Λ− , c p) = (21.9 −4.9 ± 6.5) × 10 + − + B(B → Λc pπ ) = (201 ± 105 ± 56) × 10−6 , + − −6 . B(B 0 → Λ− c pπ π ) = (1030 ± 90 ± 295) × 10
A similar hierarchy is observed in charmless baryonic decays. Two-body final states have not been observed yet with upper limits around 5 × 10−7 [9], while the branching fractions with threebody final states are around 1–5×10−6, and the branching fraction for the first four-body final state, ppK ∗+ , is about 10 × 10−6 [10]. Another interesting feature that is commonly observed in all baryonic three-body decay modes is the threshold enhancement just above the baryon-pair mass. In order to understand the
184
M. Nakao / Nuclear Physics B (Proc. Suppl.) 164 (2007) 181–184
effect, we have measured the decay angle distribution. In the case of B + → ppK + , the distribution of the cosine of the p decay angle with respect to K + shows a strong peak towards 1, and therefore the enhancement is likely to be due to a fragmentation effect. On the other + hand, in the case of B + → Λ− c pπ , the enhancement could be a new narrow bound state, since no obvious angular structure was found, with a +0.01 ± 0.02 GeV and a width of mass of 3.35 −0.02 +0.04 0.07 −0.03 ± 0.04 GeV as shown in Fig. 3.
6. Summary As discussed, Belle has reported large number of results in charmless two-body, three-body and four-body decays and various baryonic decays, among other hadronic decay modes. With the latest dataset, we have established direct CP violation in two- and three-body B decays, while the VV polarization puzzle stays with new results. Exploration of baryonic B decays continues, revealing the structure which seems to be quite different from mesonic decays.
2
Events/(0.05 GeV/c )
REFERENCES 25 20 15 10 5 0 3.2
3.4
3.6
3.8
4
4.2
4.4
4.6 –
4.8
5 2
M(Λ+cp) (GeV/c )
Figure 3. + Λ− c pπ .
+ Λ+ → c p mass distribution in B
We have also reported the observations of doubly charmed baryonic decay modes, B + → − + 0 + − 0 + Λ+ → Ξ0c Λ+ c Λc K , B → Λc Λc K [11], B c 0 − + and evidence for B → Ξc Λc [12]. The branching fractions for the first two are B(B + → +1.0 − + −4 Λ+ and c Λc K ) = (6.5 −0.9 ± 0.8 ± 3.4) × 10 +2.9 0 + − 0 B(B → Λc Λc K ) = (7.9 −2.3 ±1.2±4.2)×10−4, and the product branching fractions for the lat0 + − ter two are B(B + → Ξ0c Λ+ c ) × B(Ξc → Ξ π ) = +1.0 −5 0 + (4.8 −0.9 ±1.1±1.2)×10 and B(B → Ξ− c Λc )× +3.7 − + − − B(Ξc → Ξ π π ) = (9.3 −2.8 ± 1.9 ± 2.4)× 10−5, where the third error is due to the uncertainty − + of B(Λ+ c → pK π ). Assuming the theoretical prediction for B(Ξ0c → Ξ+ π − ), we find the −3 B(B + → Ξ0c Λ+ , which is c ) may be a few 10 a significant contribution to the total B decay width, and is much larger than the expectation for a two-body baryonic decay mode.
1. Theoretical works are not cited due to the limited space. Please refer the references in [2]–[12]. 2. Belle Collaboration, K. Abe et al., hep-ex/ 0507045. 3. Belle Collaboration, K. Abe et al., hep-ex/ 0506080, to appear in Phys. Rev. Lett. 4. Belle Collaboration, K. Abe et al., hep-ex/ 0509001. 5. Belle Collaboration, K.-F. Chen et al., hepex/0503013, to appear in Phys. Rev. Lett. 6. Belle Collaboration, J. Zhang et al., Phys. Rev. Lett. 91, 221801 (2003); Belle Collaboration, K. Abe et al., hep-ex/0507039. 7. Belle Collaboration, J. Zhang et al., Phys. Rev. Lett. 95, 141801 (2005). 8. Belle Collaboration, N. Gabyshev et al., Phys. Rev. Lett. 90, 141802 (2003); Belle Collaboration, K. Abe et al., BELLE-CONF-0468. 9. Belle Collaboration, M.-C. Chang et al., Phys. Rev. D 71, 072007 (2005). 10. Belle Collaboration, M.-Z. Wang et al., Phys. Rev. Lett. 92, 171802 (2004); Belle Collaboration, Y.-J. Lee et al., Phys. Rev. Lett. 93, 211801 (2004). 11. Belle Collaboration, K. Abe et al., hep-ex/ 0508015. 12. Belle Collaboration, R. Chistov et al., hepex/0510074.